Details

sample312.0ms

Algorithm

intervals

Results

70.0ms	48×	body	1280	valid
55.0ms	13×	body	160	valid
37.0ms	41×	body	640	valid
31.0ms	159×	body	80	valid
12.0ms	21×	body	320	valid
10.0ms	47×	body	80	nan

simplify3.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5020
7	4228
6	1403
5	705
4	360
3	169
2	91
1	46
0	20

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.0b

localize76.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.2b	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
0.3b	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
14.5b	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

rewrite305.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
22×	`add-exp-log`
19×	`*-un-lft-identity` `add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`times-frac`
7×	`unpow-prod-down` `associate-l`
6×	`associate-/r*` `prod-exp`
5×	`pow1` `div-exp`
4×	`insert-posit16` `associate-/l*` `add-log-exp`
3×	`pow-to-exp` `cbrt-undiv` `pow-unpow` `associate-r` `pow-exp` `unswap-sqr` `sqr-pow`
2×	`clear-num` `frac-2neg` `cbrt-unprod` `div-inv`
1×	`pow-pow` `tan-quot` `associate-/r/` `*-commutative`

Counts

4 → 97

Calls

4 calls:

11.0ms	(/ x (tan B))
64.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
168.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
56.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

series575.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ x (tan B))
223.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
117.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
113.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

simplify1.5s

Counts

109 → 109

Iterations

Iter	Nodes
done	5000
2	1400
1	458
0	199

prune863.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.2b	(* (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (/ 1 (sin B)))
0.3b	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
14.5b	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

rewrite368.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-exp-log`
31×	`prod-exp`
29×	`add-sqr-sqrt`
24×	`*-un-lft-identity` `add-cube-cbrt`
20×	`add-cbrt-cube`
18×	`times-frac`
16×	`associate-r`
9×	`div-exp`
8×	`associate-l`
7×	`pow1` `unpow-prod-down` `cbrt-unprod`
6×	`pow-to-exp` `pow-exp`
4×	`rec-exp` `1-exp` `insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `associate-/r` `associate-/l` `unswap-sqr` `sqr-pow`
2×	`*-commutative` `div-inv`
1×	`clear-num` `pow-pow` `frac-2neg` `pow-prod-down` `tan-quot` `associate-*r/` `associate-/r/` `un-div-inv`

Counts

4 → 119

Calls

4 calls:

12.0ms	(/ x (tan B))
167.0ms	(* (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (/ 1 (sin B)))
155.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
27.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

series648.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ x (tan B))
227.0ms	(* (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (/ 1 (sin B)))
130.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
133.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

simplify2.0s

Counts

131 → 131

Iterations

Iter	Nodes
done	5000
2	1705
1	588
0	235

prune861.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x (cos B)) (sin B))
0.2b	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
0.3b	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
14.5b	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

rewrite253.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
18×	`add-sqr-sqrt`
16×	`add-cbrt-cube`
13×	`*-un-lft-identity` `add-cube-cbrt`
7×	`unpow-prod-down` `associate-l` `prod-exp`
6×	`associate-/r*` `times-frac` `div-exp`
5×	`pow1`
4×	`cbrt-undiv` `insert-posit16` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `associate-r` `pow-exp` `cbrt-unprod` `unswap-sqr` `sqr-pow`
2×	`clear-num` `frac-2neg` `div-inv` `associate-/l*`
1×	`pow-pow` `*-commutative`

Counts

4 → 90

Calls

4 calls:

12.0ms	(/ (* x (cos B)) (sin B))
59.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
138.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
41.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

series558.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ (* x (cos B)) (sin B))
209.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
104.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
104.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

simplify1.7s

Counts

102 → 102

Iterations

Iter	Nodes
done	5001
2	1557
1	469
0	185

prune759.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ x (sin B)) (cos B))
0.2b	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
0.3b	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
14.5b	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

rewrite305.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`add-exp-log`
20×	`associate-l`
19×	`*-un-lft-identity` `add-cube-cbrt`
16×	`add-cbrt-cube`
13×	`times-frac`
8×	`prod-exp`
7×	`pow1` `unpow-prod-down`
6×	`associate-r`
5×	`div-exp` `unswap-sqr`
4×	`cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`pow-to-exp` `cbrt-undiv` `pow-unpow` `associate-/r*` `pow-exp` `sqr-pow`
2×	`*-commutative` `div-inv`
1×	`clear-num` `pow-pow` `frac-2neg` `pow-prod-down` `associate-l/` `associate-/l`

Counts

4 → 101

Calls

4 calls:

37.0ms	(* (/ x (sin B)) (cos B))
68.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
150.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
45.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

series550.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(* (/ x (sin B)) (cos B))
210.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
107.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
113.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

simplify1.4s

Counts

113 → 113

Iterations

Iter	Nodes
done	5000
2	1600
1	510
0	206

prune727.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes338.0ms

Accuracy

98.2% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 11.0b

bsearch415.0ms

Steps

Iters	Range		Point
6	0.024060934617792813	0.15022451063614659	0.14762500256041372
9	-1.3083536595822352e+23	-11403404315933134.0	-1.291039132795298e+23

simplify32.0ms

Iterations

Iter	Nodes
done	38
1	38
0	31

end0.0ms

sample10.7s

Algorithm

intervals

Results

3.8s	1683×	body	1280	valid
3.2s	1409×	body	640	valid
1.8s	4706×	body	80	valid
796.0ms	719×	body	320	valid
514.0ms	1644×	body	80	nan
249.0ms	349×	body	160	valid